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Steenrod structures on categorified quantum groups. (English) Zbl 1432.17011

In the paper under review, the authors introduce and study an interaction between Steenrod algebra and categorified quantum groups. More precisely, they extend categorified quantum groups to module categories over the Steenrod algebras \(\mathcal A_p\). Their main focus is on the \(2\)-categories \(\mathcal{U}_{\mathbb F_p}^+\) obtained from the categorification of the positive half of the quantum group \(U_q\mathfrak{sl}(2)\) by taking the coefficients of the \(2\)-morphisms in the field \(\mathbb F_p\). This categorification is the main result in [M. Khovanov and Y. Qi, Quantum Topol. 6, No. 2, 185–311 (2015; Zbl 1352.81038)], where a differential on \(\mathcal{U}_{\mathbb F_p}^+\) is introduced, which reduces it to a categorification in which \(q\) is set to a \(p\)-th root of unity. The authors show that this differential is a Margolis differential.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
55S10 Steenrod algebra

Citations:

Zbl 1352.81038

References:

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